I will create multiple sale versions of the same application with push notifications feature:
No, this is not possible. The App ID is what controls each app's capability to share keychain access.
The key here is the "...between multiple applications you build with a single App ID" portion.
App ID is not the bundle. "com.company.coolapp" is the App ID and is what controls keychain access...as well as things like whether it can be push enabled, etc.
Unfortunately what you want, it seems, is "using a wildcard App ID".
This cannot be done if you want to use push and in-app purchase.
Remember, though...Apple has frowned on having both a "Lite" version as well as an "in-app" updatable version. One or the other. Recently they have been pushing the "in-app" updatable...it makes them more money.